Question

The circumference of 2 circles are 2:3. Then what is the ratio of their area.

Answer 1

Answer:

4:9

Step-by-step explanation:

circumference of circle is 2π r

let the radius of first circle be r1

circumference of first circle = 2π r1

let radius of second circle be r2

circumference of second circle = 2π r2

ratio is 2:3

$\frac{2\pi \: r1}{2\pi \: r2} = \frac{2}{3} \\ \frac{r1}{r2} = \frac{2}{3}$

area of first circle = π r1^2

area of second circle = π r2^2

ratio of areas

$\frac{\pi {r1}^{2} }{\pi {r2}^{2} } \\ = \frac{ {r1}^{2} }{ {r2}^{2} } \\ = \frac{ {2}^{2} }{ {3}^{2} } \: \: \: (since \: \frac{r1}{r2} = \frac{2}{3} ) \\ = \frac{4}{9}$

therefore the ratio of the areas of circle is 4:9

hope you get your answer